GL(2, ) Structures, -Geometry and Twister Theory

Abstract

In this research we study the curvature of almost Hermition manifolds and their special analogues via intrnsic torsion and representation theory. We also investigate that the compact 7-dimensional manifold equipped with G_2-Structure with closed fundamental form is Einstein if and only if the Riemannian holonomy of the induced metric is contained in G_2. Also we illustrate that Bryant’s weak holonomy metric on the homology seven-sphere is the unique weak metric arising from a rational curve.